What you have done is; using the mkdir command you created a new directory called public_html.
Then using the chmod command you changed the access permissions for this new directory.
The change directroy command (cd) moved you into the new directory.
By touching index.html you created a new empty file.
The chmod command again assigned new permissions for access to index.html, which is your empty homepage.
the list command (el es space minus el) now shows your index.html on the screen in the public_html directory with access permissions correct.
Don't forget to include the tilde (~) in front of your userid. This is neccessary. Also in your public_html there is an underline character between the words. These are musts.